The official Twitter accounts of the Congress party and its vice president Rahul Gandhi appeared to have been hacked on Thursday.
Mr. Gandhi's account came under a similar attack on Wednesday, with a series of obscene tweets posted on the timeline.
The Congress leader has filed a police complaint in connection with the Wednesday's attack.
"A complaint was lodged by Congress leader R.S. Surjewala on behalf of Mr. Gandhi late on Wednesday night. We are in the process registering an FIR," said Additional Deputy Commissioner of Police (Cyber Cell) Anyesh Roy.